The given series is
\[
\sum_{k=0}^{100} \frac{(-1)^k}{2 k!}\left(\frac{5 \pi}{4}\right)^{2 k}
\]
This resembles the Maclaurin series for the exponential function \(e^x\), which is
\[
e^x = \sum_{k=0}^{\infty} \frac{x^k}{k!}
\]
However, the series given is
Show more…